First, make sure you save your game right after the fight starts, if you do happen to die, just reload your savegame and the achievement will still unlock.
Like most bosses in this game, the trick to defeating the Torso Boss is to fill his rage bar. He will do a variation of 2 attacks. He will either summersault at you, trying to squash you with his body, or try and hit you with his massive hands.
The area where you will fight this boss will be closed off by walls, except for 1 side, where there will be a lava pit beneath you. The first time you fill up the boss' rage meter, make sure you stand in front of the pit. He will summersault right into it, but will manage to hang on to the edge with his left hand. Shooting his hand at this moment will help, but you will not be able to shoot him down before he manages to pull himself up.
Filling up his rage meter again, the boss will try the handsmash, after the adrenaline attack his hand will get stuck in the floor, at which time you can target his left hand. He will however smash the floor with his other hand, knocking Lara to the ground, so jump up whenever he does this. Keep shooting until you get a cinematic of him clutching his hand.
As you may have guessed, your main target will be his left hand, keep shooting it every chance you get until he can't clutch onto the ledge anymore and falls into the lava pit below.